Cook the liver and onions. Heat the clarified butter in a skillet until melted. Add the onions and liver pieces. Sauté until the livers are browned and the onions are tender.
Season the liver mixture. Add the wine, garlic, mustard, herbs, and lemon juice and cook uncovered until most of the liquid has evaporated. Set aside to cool.
Grind the mixture into a smooth paste. Scrape the cooled liver mixture into a food processor and add the butter. Blend until smooth. If the pâté is dry and crumbly rather than smooth and creamy, add more butter one tablespoon at a time. Add salt and pepper to taste.
Chill and serve. Place the pâté in a serving dish and grind a generous amount of cracked pepper over the top. Serve immediately, if desired, but preferably, set in the fridge for a few hours or overnight, as the best flavor will be after a day or two. Bring to room temperature prior to serving. Serve with sourdough toasts or whole grain crackers.